Portal de Periódicos da CAPES

Reconstruction of the genesis of a Renaissance algorithm to calculate sine tables

2019; Wiley; Volume: 19; Issue: 1 Linguagem: Inglês

10.1002/pamm.201900013

1617-7061

Peter Ullrich,

Medical and Biological Sciences

Abstract Recently, a manuscript has been discovered in which Jost Bürgi (1552–1632) presented an algorithm to calculate sine tables of high precision with only a modest amount of numerical effort [1], [2]. Several modern proofs for the correctness of this algorithm have been given, all of which, however, use methods that were not at hand at Bürgi's time. This raises the question how Bürgi had found his algorithm. Building on [5], an educated guess is presented how Bürgi may have found his algorithm and also collected enough evidence for its correctness. For this, only methods are needed which were known at Bürgi's time, like prosthaphaeresis and the method of false position.